Home
Class 12
MATHS
Evaluate |{:(1,x,y),(1,x+y,y),(1,x,x+y):...

Evaluate `|{:(1,x,y),(1,x+y,y),(1,x,x+y):}|`

Text Solution

Verified by Experts

The correct Answer is:
xy
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Practice Work|90 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|42 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Exercise 4.6|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 5 (Section-D)|4 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER-7 (SECTION-D)|2 Videos

Similar Questions

Explore conceptually related problems

Evaluate |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(a+x,y,z),(x,a+y,z),(x,y,a+z):}|

|{:(x,1,y+z),(y,1,z+x),(z,1,x+y):}|=.......

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z):}|

Without expanding prove that Delta=|{:(x+y,y+z,z+x),(z,x,y),(1,1,1):}|=0

If x,y,z are all different from zero and |{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=0 then value of x^(-1)+y^(-1)+z^(-1) is ".........."

If the co-ordinates of the vertices of an equilateral trianlg with sides of length 'a' are (x_1,y_1),(x_2,y_2),(x_3,y_3) , then Prove that |{:(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1):}|^2=(3/4)a^4.

Evaluate |{:(.^(x)C_(1),,.^(x)C_(2),,.^(x)C_(3)),(.^(y)C_(1),,.^(y)C_(2),,.^(y)C_(3)),(.^(x)C_(1),,.^(z)C_(2),,.^(z)C_(3)):}|

If A(x_(1), y_(1)), B(x_(2), y_(2)) and C (x_(3), y_(3)) are the vertices of a Delta ABC and (x, y) be a point on the internal bisector of angle A, then prove that b|(x,y,1),(x_(1),y_(1),1),(x_(2),y_(2),1)|+c|(x,y,1),(x_(1),y_(1),1),(x_(3),y_(3),1)|=0 where, AC = b and AB = c.

An equilateral triangle has each side equal to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinant |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals

KUMAR PRAKASHAN-DETERMINANTS -MISCELLANEOUS EXERCISE - 4
  1. Prove that the determinent |{:(x,sintheta,costheta),(-sintheta,-x,1),(...

    Text Solution

    |

  2. Without expanding the determinant prove that |{:(a,a^2,bc),(b,b^2,ca),...

    Text Solution

    |

  3. Evaluate |{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosb...

    Text Solution

    |

  4. If a, b and c are real numbers , and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b...

    Text Solution

    |

  5. Solve the equation |{:(x+a,x,x),(x,x+a,x),(x,x,x+a):}|=0. (ane0)

    Text Solution

    |

  6. Prove that |{:(a^2,bc,ac+c^2),(a^2+ab,b^2,ac),(ab,b^2+bc,c^2):}|=4a^2b...

    Text Solution

    |

  7. If A^(-1)=[{:(3,-1,1),(-15,6,-5),(5,-2,2):}] and B=[{:(1,2,-2),(-1,3,0...

    Text Solution

    |

  8. Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}] Verify that [adjA]^(-1)=adj(A^...

    Text Solution

    |

  9. Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}] Verify that (A^(-1))^-1=A

    Text Solution

    |

  10. Evaluate |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|

    Text Solution

    |

  11. Evaluate |{:(1,x,y),(1,x+y,y),(1,x,x+y):}|

    Text Solution

    |

  12. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  13. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  14. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  15. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  16. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  17. Solve the following system of linear equations 2/x+3/y+(10)/z=4 4/...

    Text Solution

    |

  18. If a,b,c are in A.P then the determinant |{:(x+2,x+3,x+2a),(x+3,x+4,...

    Text Solution

    |

  19. If x,y,z are nonzero real numbers, then the inverse of matrix A=[{:(x,...

    Text Solution

    |

  20. Let A=[{:(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1):}] w...

    Text Solution

    |